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Re: Simplification to Partial Fractions

  • To: mathgroup at smc.vnet.net
  • Subject: [mg59699] Re: [mg59676] Simplification to Partial Fractions
  • From: "Jon Palmer" <jonathan.palmer at new.oxford.ac.uk>
  • Date: Thu, 18 Aug 2005 00:16:32 -0400 (EDT)
  • Reply-to: <jonathan.palmer at new.oxford.ac.uk>
  • Sender: owner-wri-mathgroup at wolfram.com

At first glance I can't make PolynomialReduce do what I need.

Here is an example problem. Take the expression:

u1 = A + (B*(x^2 - y^2)^2)/(x^2 + y^2) +  (C*(y^2 - z^2)^2)/(y^2 + z^2)
 + (D*(-x^2 + z^2)^2)/(x^2 + z^2) 

Now 

u2 = Factor[u1]



How do you Simplify u2 back to the form of u1? 

Many thanks
Jon Palmer




> -----Original Message-----
> From: Andrzej Kozlowski [mailto:akoz at mimuw.edu.pl]
To: mathgroup at smc.vnet.net
> Sent: Wednesday, August 17, 2005 11:14 AM
> Cc: mathgroup at smc.vnet.net
> Subject: [mg59699] Re: [mg59676] Simplification to Partial Fractions
> 
> 
> On 17 Aug 2005, at 10:00, Jon Palmer wrote:
> 
> > I was wondering if someone can help with a Partial Fraction problem.
> >
> > I have a calculated expression, u, which is a quotient of two
> > polynomials in
> > three variables x, y & z.
> >
> >
> > u = P(x,y,z)/Q(x,y,z)
> >
> >
> > I know that the quotient, when simplified, is a sum of partial
> > fractions of
> > the form
> >
> > u = R(x,y,z) + S(x,y,z)/(x^2 +y^2)  + T(x,y,z)/(y^2 +z^2) + U
> > (x,y,z)/(z^2
> > +x^2)
> >
> >
> > Is there a way to simplify the expression into the parial fraction
> > form?
> >
> > I have tried various combinations of Simplify, Apart, Collect etc.
> > and can't
> > find a method that works. Any help would be much appreciated.
> >
> > Thanks
> > Jon Palmer
> >
> >
> 
> It should be possible to do this using PolynomialReduce but you would
> have to post the actual problem before I could tell for sure.
> 
> Andrzej Kozlowski



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